Consider the directed graph shown in the figure below. There are multiple shortest paths between vertices S and T. Which one will be reported by Dijkstra’s shortest path algorithm? Assume that, in any iteration, the shortest path to a vertex v is updated only when a strictly shorter path to v is discovered.

An undirected graph G(V, E) contains n ( n > 2 ) nodes named v₁ , v₂ ,….v_n. Two nodes v_i , v_j are connected if and only if 0 < |i – j| <= 2. Each edge (v_i, v_j ) is assigned a weight i + j. A sample graph with n = 4 is shown below. What will be the cost of the minimum spanning tree (MST) of such a graph with n nodes?

An undirected graph G(V, E) contains n ( n > 2 ) nodes named v₁ , v₂ ,….v_n. Two nodes v_i , v_j are connected if and only if 0 < |i – j| <= 2. Each edge (v_i, v_j ) is assigned a weight i + j. A sample graph with n = 4 is shown below. The length of the path from v5 to v6 in the MST of previous question with n = 10 is

Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry W(ij) in the matrix W below is the weight of the edge {i, j}. $$$w = \left( {\matrix{ 0 & 1 & 8 & 1 & 4 \cr 1 & 0 & {12} & 4 & 9 \cr 8 & {12} & 0 & 7 & 3 \cr 1 & 4 & 7 & 0 & 2 \cr 4 & 9 & 3 & 2 & 0 \cr } } \right)$$$ What is the minimum possible weight of a spanning tree T in this graph such that vertex 0 is a leaf node in the tree T?